Using uncertainty quantification to develop vehicle prototypes.

Uncertainty is by its very nature non-intuitive and, according to research conducted by the Uncertainty Quantification and Management Special Interest Group (UQ&M SIG), “The difficulties in effectively communicating the results of uncertainty quantification studies are a significant roadblock to the more widespread adoption of UQ techniques”.

The inability to effectually communicate the outputs of a UQ process can render the entire process redundant.

Why is it difficult?

According to Ken Brodlie in A Review of Uncertainty in Data Visualisation, the difficulties are:

Uncertainty is complex: “Uncertainty, by its very nature, is a difficult subject … even the terminology is often unhelpful.”Uncertainty information is presented in different ways: for example, “as a probability density function, as multivalue data, as bounded data, and other representations”.Uncertainty propagates: “When we calculate with uncertain data, we propagate the uncertainty … We need to understand how to propagate uncertainty in the data, through to uncertainty in [an] image.Uncertainty adds a dimension to the visualisation: “We have enough problems visualising exact 3-dimensional or higher dimensional data without introducing another dimension for uncertainty.”Uncertainty tends to dominate certainty: “In most natural visual representations of uncertainty, the greatest emphasis is placed on data of greatest uncertainty.”Uncertainty adds another discipline: “Some of the best visualisations have been created by multidisciplinary teams, bringing together domain scientists, numerical analysts, visualisation scientists and artists. There is a further discipline to be added now: statistics.”

The automotive industry uses prototypes as an early stage design tool. In producing prototypes, the dynamics of the vehicle – including how it rides, steers and handles – are key. The ultimate objective in the early design stage is sign-off of prototype vehicles.

But the sign-off process has its limitations. Because of the high cost of prototypes, only a set number of vehicle variants are considered. The performance variability across the full range of variants and specifications is not considered. For example, each individual vehicle will have different mass and inertia properties affecting the ride performance.

Visualising the effect uncertainty has on the ride metrics is vital to be able to communicate the outputs of an uncertainty analysis to aid the decision-making process.

The process

The assessment process measures a vehicle virtually over a range of standard ride surfaces and extracts a series of metrics, which are used to quantify the ride attribute performance during development. These metrics have been developed to reflect subjective vehicle assessment through objective measurement.

Uncertainty Quantification and Management considerations

Uncertainties could include mass properties such as distribution, centres of gravity, roll inertia, etc. Because only a limited number of prototypes are available for tuning, current ride tuning does not optimise all possible variants and specifications. Therefore, it is not fully understood how these variations in mass properties affect the ride from vehicle to vehicle.

The challenges

How can a process to optimise vehicle ride performance for all potential customer vehicle variants and option specifications be determined? How can predictions of ride variations be improved to minimise the number of variables required to achieve the desired ride performance across the programme? Is there a more effective method to optimise ride performance across a range of uncertain mass properties?

The approach

The ride performance of each variant can be predicted using a computer model that simulates vehicle performance and produces a series of ride metrics. However, due to computational expense, it is difficult to predict the values of the response variables for a large number of variants. Instead, statistical models that act as computationally cheap surrogates for the computer model are used.

Using Gaussian process models (or emulators), built from model runs selected as a space-filling design, it is possible to predict vehicle ride performance for vehicles for which the computational model has not been run.

For visualisation purposes (the subject of this article), user interfaces were created to to allow easy interrogation of the surrogates to enable the user to choose to generate and view predicted ride metrics for one or more of the variants, including uncertainty estimates.

This visualisation approach allows the user to intuitively explore the effect uncertainty has on design metrics, to aid in design studies and future decision making.

The benefits

Allowing the user to explore the effect uncertainty has on the ride metrics can aid in the design and decision making process. This then leads to greater confidence in the overall goals of such a vehicle dynamics study:

Optimising vehicle ride performance for all potential customer vehicle variants and option specificationsImproving prediction of ride variation to minimise the number of component variables required to achieve desired ride performance across the programme.